Spectral structure and subdecomposability of $p$-hyponormal operators

We prove that for every $p$-hyponormal operator $A, 0<p\le 1,$ there corresponds a hyponormal operator $\tilde A$ such that $A$ and $\tilde A$ have ``equal spectral structure". We also prove that every $p$-hyponormal operator $A,0<p\le 1,$ is subdecomposable. Then some relevant quasisimilarity results are obtained, including that two quasisimilar $p$-hyponormal operators have equal essential spectra.